new here plus a question...

[Magnus Danielson]

From: Don Tillman <don at till.com>
Subject: Re: new here plus a question...
Date: Sun, 21 Jan 2001 16:13:47 -0800 (PST)

>    Date: Sun, 21 Jan 2001 19:02:06 +0100
>    From: Magnus Danielson <cfmd at swipnet.se>
> 
>    From: Don Tillman <don at till.com>
>    Date: Sun, 21 Jan 2001 02:24:41 -0800 (PST)
> 
>    > I think the main issue is that translating from the s-plane to the
>    > z-plane is a very rude approximation.  z-poles are inherently
>    > different than s-poles, they won't sound the same as the original, and
>    > I'll bet you would have no problem telling the difference between the
>    > frequency response plots visually.
> 
>    z-plane and z-poles has IMHO nothing to do with it. If they do, please
>    explain.
> 
> We're talking about a digital implementation of a given linear analog
> filter circuit, right?

That single piece of information was missing. We where not discussing
the same thing...

> In the analog universe we have poles and zeroes in the s-plane, and
> the resulting frequency and phase responses that we know so well.  
> 
> In the digital universe, the poles and zeroes are in the z-plane, and
> the effect of each of these poles and zeroes can be seen in the
> resulting frequency and phase responses, but these effects are
> different from what you have in the analog universe because the
> digital filter mechanism is fundamentally different.
> 
> Further, in translating the positions of the analog poles and zeroes
> to their z-plane equivalents (the bilinear transform) things get moved
> around.
> 
> (That's a gruesome distillation of Oppenheim and Schafer's "Digital
> Signal Processing", chapters 2 and 5.)

IMHO I think that the Rabiner and Gold "Theory and Application of
Digital Signal Processing" (the twin-sister book of Oppenheim and
Schafer) gives a better description of the bilinear transforms and its
quirks. However, you will find both of these books next to each other
in my library.

Also, even if the bilinear transform does a good job, there are other
tranforms to consider.

Modeling the arctan distorsion in digital is IMHO somewhat trickier
than getting the poles and zeros in the right spot. Keeping "live" CV
of frequency and Q is a bit tricky too.

Cheers,
Magnus